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Eye tracking is an increasingly popular method in mathematics education. While the technology has greatly evolved in recent years, there is a debate about the specific benefits that eye tracking offers and about the kinds of insights it may allow. The aim of this review is to contribute to this discussion by providing a comprehensive overview of the use of eye tracking in mathematics education research. We reviewed 161 eye-tracking studies published between 1921 and 2018 to assess what domains and topics were addressed, how the method was used, and how eye movements were related to mathematical thinking and learning. The results show that most studies were in the domain of numbers and arithmetic, but that a large variety of other areas of mathematics education research was investigated as well. We identify a need to report more methodological details in eye-tracking studies and to be more critical about how to gather, analyze, and interpret eye-tracking data. In conclusion, eye tracking seemed particularly beneficial for studying processes rather than outcomes, for revealing mental representations, and for assessing subconscious aspects of mathematical thinking.
Professional knowledge is highlighted as an important prerequisite of both medical doctors and teachers. Based on recent conceptions of professional knowledge in these fields, knowledge can be differentiated within several aspects. However, these knowledge aspects are currently conceptualized differently across different domains and projects. Thus, this paper describes recent frameworks for professional knowledge in medical and educational sciences, which are then integrated into an interdisciplinary two-dimensional model of professional knowledge that can help to align terminology in both domains and compare research results. The models’ two dimensions differentiate between cognitive types of knowledge and content-related knowledge facets and introduces a terminology for all emerging knowledge aspects. The models’ applicability for medical and educational sciences is demonstrated in the context of diagnosis by describing prototypical diagnostic settings for medical doctors as well as for teachers, which illustrate how the framework can be applied and operationalized in these areas. Subsequently, the role of the different knowledge aspects for acting and the possibility of transfer between different content areas are discussed. In conclusion, a possible extension of the model along a “third dimension” that focuses on the effects of growing expertise on professional knowledge over time is proposed and issues for further research are outlined.
Diagnostic competences are an essential facet of teacher competence. Many studies have investigated the quality of teachers’ judgments of students’ competences. However, little is known about the processes that lead to these judgments and about the ways to promote these processes in the early phase of teacher training. The aim of the research project on which we report in this paper was to develop a simulated computer-based environment that allows assessing and promoting the diagnostic processes of prospective teachers. In the simulated environment, ‘virtual third-graders’ solve mathematical problems. Participants are asked to diagnose the students’ competence levels according to a theoretical model, which has been empirically validated. Participants can repeatedly select mathematical problems of varying difficulty levels, assign them to a virtual student, and then receive the student’s written solution. In this paper, we present the conceptualization of the simulated environment. We also report on the results of a pilot study with 91 prospective primary school mathematics teachers to analyze whether the environment allows an assessment of individual differences in diagnostic processes. The majority of participants rated the environment as authentic and as one in which they could become immersed. Overall, participants were fairly accurate in their diagnoses concerning the student’s competence level. However, log data and participants’ written notes indicated that there was large variability in their diagnostic processes. Participants varied greatly in the number of mathematical problems they assigned to a student during their diagnostic process, and in how strongly the difficulty of these problems deviated from the student’s true competence level. Overall, the data suggest that the simulated environment has the potential to assess diagnostic processes in a valid way. We discuss open questions and issues for further development.
Mathematics teachers’ motivational and emotional orientations regarding digital tools in mathematics classrooms are key aspects influencing whether and how technology is used to teach mathematics—making the support of those characteristics one central goal for teacher education. In this article we investigated if and how a workshop-based in-service teacher training can foster teachers’ perceived value of digital media in mathematics education, their self-efficacy, and their anxiety towards teaching mathematics with digital tools. In an intervention study with N = 83 in-service teachers with varying teaching experience, we used cluster analysis based on their experience, value, self-efficacy, and anxiety before the intervention to determine three different teacher orientations regarding teaching mathematics with digital tools. Paired sample t-tests with pretest and posttest data revealed that for two of three clusters these beliefs, motivation, and emotions changed in a positive way during the intervention while for the third no change was found. Our study sheds light on the role of motivational and emotional orientations for the implementation of digital tools in mathematics education: it shows that these orientations can be utilized to cluster teachers on this topic and illustrates that these orientations can be successfully fostered—while individual differences may exist in the effect and success of interventions.
Abstract
Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.